On the Near-Field Spherical Wave Formation in Resonant Leaky-Wave Antennas: Application to Small Lens Design

In this work, we show that the near field of leaky-wave resonant antennas (LWAs) radiating into a dense medium can be locally represented as a spherical wave in a certain solid angle around broadside using an accurate definition of the phase center. The near field in this solid angle can be efficiently evaluated through the integration of the spectral Green’s function along the steepest descent path (SDP). Beyond this solid angle, defined as the shadow boundary angle, a residual contribution due to the leaky-wave pole must also be added to fully describe the near field. It is found that this shadow boundary angle can be used to define the phase center and geometry of a truncated lens that couples well to leaky-wave antennas, even in electrically small-to-medium sized lenses and low-contrast cases. To demonstrate the applicability of the proposed study, we combine the SDP field calculation with a Fourier optics (FO) methodology to evaluate the aperture efficiency and radiation patterns of small-to-medium sized lenses in reception. A truncated silicon lens with a diameter of only four free-space wavelengths is presented with almost 80% aperture efficiency. Excellent agreement with full-wave simulations is achieved, which demonstrates the accuracy of the proposed design and analysis methodology.